Verifiable and Collusion-Resistant Multi-Party Quantum Private Set Operations

2026-06-26

AI Summary

This work proposes the first multi-party quantum threshold private set intersection (TPSI) protocol that eliminates the need for a third party to semantically interpret results—a limitation of existing schemes that are vulnerable to collusion attacks and deviate from the core paradigm of threshold decision based solely on intersection cardinality. The protocol constructs hidden labeled measurement vectors through data rotation, masking, and aggregation of single-photon sequences, and integrates oblivious linear evaluation (OLE)-based inner product computation with lightweight garbled circuits to enable verifiable threshold evaluation and conditional intersection reconstruction without revealing semantic information. Theoretical analysis guarantees correctness and security, while feasibility is demonstrated via IBM Qiskit simulations, significantly enhancing collusion resistance and privacy preservation.

Abstract

Threshold private set intersection (TPSI) allows parties to reveal their intersection only when its cardinality reaches a prescribed threshold. Existing quantum TPSI protocols typically rely on a third party (TP) to interpret the final results, which deviates from the cardinality-testing paradigm of TPSI. In this paper, we propose a quantum multiparty TPSI protocol with explicit cardinality testing. Our protocol develops a rotation-based quantum construction in which single-photon sequences are sequentially processed through participant-side data rotations, TP--participant masking rotations, and correlated aggregate rotations. This design produces hidden-label measurement vectors: TP can complete the final measurement, but cannot interpret the semantic meaning of the outcomes. Based on these hidden measurements, we further realize the threshold decision through an oblivious linear evaluation (OLE)-based inner product procedure and a lightweight garbled circuit, revealing only \(\mathbf 1[|\bigcap_i X_i|\ge τ]\) before conditional intersection reconstruction. We prove the correctness and security of the proposed protocol, and further validate its feasibility through quantum-circuit simulations implemented on the IBM \textsf{Qiskit} platform.

Problem

• Threshold Private Set Intersection
• Quantum Multi-Party Computation
• Collusion Resistance
• Verifiability
• Cardinality Testing

Innovation

• quantum TPSI
• rotation-based quantum construction
• hidden-label measurement
• oblivious linear evaluation
• collusion-resistant